Long-time derivation of the Boltzmann equation from particle dynamics

Establish the derivation of the Boltzmann equation from a system of particles undergoing elastic collisions for large times, providing a rigorous connection between discrete dynamics and the Boltzmann kinetic equation beyond short-time regimes.

Background

To motivate the use of soft repulsive potentials and mean-field approaches, the authors remark on the broader difficulty of rigorously deriving continuum equations from particle systems with hard contact interactions.

Even in classical kinetic theory, the rigorous derivation of the Boltzmann equation from Newtonian particle systems with elastic collisions remains unresolved in large-time regimes, which underscores the mathematical challenges of coarse-graining contact interactions.